On the Stability of Markov Chains

This talk will detail the stability of Markov chains. One measure of stability of a time homogeneous Markov chain is a mixing time. I will define similar measures for special types of time inhomogeneous Markov chains called the adiabatic and stable adiabatic times. I will discuss the use of these Markov chains and I will discuss how the adiabatic and stable adiabatic times relate to mixing times. This talk is an exploration of linear algebra, analysis and probability.